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| Titel |
Approximate asymptotic integration of a higher order water-wave equation using the inverse scattering transform |
| VerfasserIn |
A. R. Osborne |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 4, no. 1 ; Nr. 4, no. 1, S.29-53 |
| Datensatznummer |
250001459
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| Publikation (Nr.) |
 copernicus.org/npg-4-29-1997.pdf |
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| Zusammenfassung |
| The complete mathematical
and physical
characterization of nonlinear water wave dynamics has
been an
important goal since the fundamental partial
differential
equations were discovered by Euler over 200 years ago.
Here I
study a subset of the full solutions by
considering the
irrotational, unidirectional multiscale expansion of
these
equations in shallow-water. I seek to integrate the
first
higher-order wave equation, beyond the order of the
Korteweg-
deVries equation, using the inverse scattering
transform.
While I am unable to integrate this equation
directly, I am
instead able to integrate an analogous equation in a
closely
related hierarchy. This new integrable wave equation is
tested
for physical validity by comparing its linear
dispersion
relation and solitary wave solution with those of
the full
water wave equations and with laboratory data. The
comparison
is remarkably close and thus supports the
physical
applicability of the new equation. These
results are
surprising because the inverse scattering
transform, long
thought to be useful for solving only very special,
low-order
nonlinear wave equations, can now be thought of as a
useful
tool for approximately integrating a wide variety of
physical
systems to higher order. I give a simple scenario for
adapting
these results to the nonlinear Fourier
analysis of
experimentally measured wave trains. |
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